On the thermodynamics of a superconducting ring interrupted by a weak superconducting junction: III. Thermodynamic fluctuations

A superconducting ring interrupted by a weak Josephson junction can have two metastable magnetic flux states separated by a potential energy barrier in case an external magnetic field of appropriate strength is applied. In a previous article, part I, the thermodynamic Gibbs surface of this system was constructed together with the relevant contribution to the entropy being the negative of the corresponding partial derivative of the Gibbs function, while in part II the magnetic availability of this system, being the minimum work an external source must perform to bring the small system reversibly from a state of equilibrium with the surroundings to a given non-equilibrium state, was constructed. Calculations were presented of relevance in intepreting thermodynamic fluctuation phenomena of the total embraced flux which are determined by the potential magnetic availability of the system with respect to the surroundings fixed by the temperature of the heat reservoir and the external magnetic field. In the present article (part III) it is argued that the probability of the equilibrium steady state solution is determined by the total dynamic availability of the system, containing contributions both from the potential availability and from the kinetic energy. The total dynamic availability is a function of the fluctuating parameters: the embraced flux, the flux velocity and the local temperature of the junction. In order to find the distribution in the magnetic flux alone the other variables, the flux velocity and the temperature are integrated out by numerical methods.